Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2775530621\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.14148 | −1.23639 | −0.618193 | − | 0.786026i | \(-0.712135\pi\) | ||||
−0.618193 | + | 0.786026i | \(0.712135\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.02625 | 1.35338 | 0.676691 | − | 0.736267i | \(-0.263413\pi\) | ||||
0.676691 | + | 0.736267i | \(0.263413\pi\) | |||||||
\(6\) | −2.14148 | −0.874257 | ||||||||
\(7\) | 4.90651 | 1.85448 | 0.927242 | − | 0.374462i | \(-0.122173\pi\) | ||||
0.927242 | + | 0.374462i | \(0.122173\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.58595 | 0.528650 | ||||||||
\(10\) | 3.02625 | 0.956985 | ||||||||
\(11\) | 2.36471 | 0.712986 | 0.356493 | − | 0.934298i | \(-0.383972\pi\) | ||||
0.356493 | + | 0.934298i | \(0.383972\pi\) | |||||||
\(12\) | −2.14148 | −0.618193 | ||||||||
\(13\) | 2.98785 | 0.828680 | 0.414340 | − | 0.910122i | \(-0.364012\pi\) | ||||
0.414340 | + | 0.910122i | \(0.364012\pi\) | |||||||
\(14\) | 4.90651 | 1.31132 | ||||||||
\(15\) | −6.48067 | −1.67330 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.102887 | 0.0249538 | 0.0124769 | − | 0.999922i | \(-0.496028\pi\) | ||||
0.0124769 | + | 0.999922i | \(0.496028\pi\) | |||||||
\(18\) | 1.58595 | 0.373812 | ||||||||
\(19\) | 0.460748 | 0.105703 | 0.0528514 | − | 0.998602i | \(-0.483169\pi\) | ||||
0.0528514 | + | 0.998602i | \(0.483169\pi\) | |||||||
\(20\) | 3.02625 | 0.676691 | ||||||||
\(21\) | −10.5072 | −2.29286 | ||||||||
\(22\) | 2.36471 | 0.504157 | ||||||||
\(23\) | 0.572097 | 0.119290 | 0.0596452 | − | 0.998220i | \(-0.481003\pi\) | ||||
0.0596452 | + | 0.998220i | \(0.481003\pi\) | |||||||
\(24\) | −2.14148 | −0.437128 | ||||||||
\(25\) | 4.15821 | 0.831641 | ||||||||
\(26\) | 2.98785 | 0.585965 | ||||||||
\(27\) | 3.02817 | 0.582771 | ||||||||
\(28\) | 4.90651 | 0.927242 | ||||||||
\(29\) | −4.49268 | −0.834270 | −0.417135 | − | 0.908844i | \(-0.636966\pi\) | ||||
−0.417135 | + | 0.908844i | \(0.636966\pi\) | |||||||
\(30\) | −6.48067 | −1.18320 | ||||||||
\(31\) | −1.20673 | −0.216735 | −0.108367 | − | 0.994111i | \(-0.534562\pi\) | ||||
−0.108367 | + | 0.994111i | \(0.534562\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.06398 | −0.881526 | ||||||||
\(34\) | 0.102887 | 0.0176450 | ||||||||
\(35\) | 14.8483 | 2.50982 | ||||||||
\(36\) | 1.58595 | 0.264325 | ||||||||
\(37\) | −1.90370 | −0.312966 | −0.156483 | − | 0.987681i | \(-0.550016\pi\) | ||||
−0.156483 | + | 0.987681i | \(0.550016\pi\) | |||||||
\(38\) | 0.460748 | 0.0747432 | ||||||||
\(39\) | −6.39843 | −1.02457 | ||||||||
\(40\) | 3.02625 | 0.478493 | ||||||||
\(41\) | 11.7432 | 1.83398 | 0.916988 | − | 0.398916i | \(-0.130613\pi\) | ||||
0.916988 | + | 0.398916i | \(0.130613\pi\) | |||||||
\(42\) | −10.5072 | −1.62130 | ||||||||
\(43\) | 7.15540 | 1.09119 | 0.545594 | − | 0.838050i | \(-0.316304\pi\) | ||||
0.545594 | + | 0.838050i | \(0.316304\pi\) | |||||||
\(44\) | 2.36471 | 0.356493 | ||||||||
\(45\) | 4.79948 | 0.715465 | ||||||||
\(46\) | 0.572097 | 0.0843511 | ||||||||
\(47\) | −2.47929 | −0.361642 | −0.180821 | − | 0.983516i | \(-0.557875\pi\) | ||||
−0.180821 | + | 0.983516i | \(0.557875\pi\) | |||||||
\(48\) | −2.14148 | −0.309096 | ||||||||
\(49\) | 17.0738 | 2.43911 | ||||||||
\(50\) | 4.15821 | 0.588059 | ||||||||
\(51\) | −0.220331 | −0.0308525 | ||||||||
\(52\) | 2.98785 | 0.414340 | ||||||||
\(53\) | 6.38183 | 0.876612 | 0.438306 | − | 0.898826i | \(-0.355579\pi\) | ||||
0.438306 | + | 0.898826i | \(0.355579\pi\) | |||||||
\(54\) | 3.02817 | 0.412081 | ||||||||
\(55\) | 7.15620 | 0.964942 | ||||||||
\(56\) | 4.90651 | 0.655659 | ||||||||
\(57\) | −0.986685 | −0.130690 | ||||||||
\(58\) | −4.49268 | −0.589918 | ||||||||
\(59\) | −6.28216 | −0.817867 | −0.408934 | − | 0.912564i | \(-0.634099\pi\) | ||||
−0.408934 | + | 0.912564i | \(0.634099\pi\) | |||||||
\(60\) | −6.48067 | −0.836651 | ||||||||
\(61\) | −10.0775 | −1.29030 | −0.645148 | − | 0.764058i | \(-0.723204\pi\) | ||||
−0.645148 | + | 0.764058i | \(0.723204\pi\) | |||||||
\(62\) | −1.20673 | −0.153255 | ||||||||
\(63\) | 7.78147 | 0.980373 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.04198 | 1.12152 | ||||||||
\(66\) | −5.06398 | −0.623333 | ||||||||
\(67\) | −0.866688 | −0.105883 | −0.0529414 | − | 0.998598i | \(-0.516860\pi\) | ||||
−0.0529414 | + | 0.998598i | \(0.516860\pi\) | |||||||
\(68\) | 0.102887 | 0.0124769 | ||||||||
\(69\) | −1.22514 | −0.147489 | ||||||||
\(70\) | 14.8483 | 1.77471 | ||||||||
\(71\) | −10.2469 | −1.21609 | −0.608045 | − | 0.793903i | \(-0.708046\pi\) | ||||
−0.608045 | + | 0.793903i | \(0.708046\pi\) | |||||||
\(72\) | 1.58595 | 0.186906 | ||||||||
\(73\) | 0.484504 | 0.0567070 | 0.0283535 | − | 0.999598i | \(-0.490974\pi\) | ||||
0.0283535 | + | 0.999598i | \(0.490974\pi\) | |||||||
\(74\) | −1.90370 | −0.221300 | ||||||||
\(75\) | −8.90473 | −1.02823 | ||||||||
\(76\) | 0.460748 | 0.0528514 | ||||||||
\(77\) | 11.6025 | 1.32222 | ||||||||
\(78\) | −6.39843 | −0.724479 | ||||||||
\(79\) | −1.79064 | −0.201463 | −0.100732 | − | 0.994914i | \(-0.532118\pi\) | ||||
−0.100732 | + | 0.994914i | \(0.532118\pi\) | |||||||
\(80\) | 3.02625 | 0.338345 | ||||||||
\(81\) | −11.2426 | −1.24918 | ||||||||
\(82\) | 11.7432 | 1.29682 | ||||||||
\(83\) | −8.29759 | −0.910779 | −0.455389 | − | 0.890292i | \(-0.650500\pi\) | ||||
−0.455389 | + | 0.890292i | \(0.650500\pi\) | |||||||
\(84\) | −10.5072 | −1.14643 | ||||||||
\(85\) | 0.311363 | 0.0337720 | ||||||||
\(86\) | 7.15540 | 0.771586 | ||||||||
\(87\) | 9.62100 | 1.03148 | ||||||||
\(88\) | 2.36471 | 0.252079 | ||||||||
\(89\) | 6.42816 | 0.681384 | 0.340692 | − | 0.940175i | \(-0.389339\pi\) | ||||
0.340692 | + | 0.940175i | \(0.389339\pi\) | |||||||
\(90\) | 4.79948 | 0.505910 | ||||||||
\(91\) | 14.6599 | 1.53677 | ||||||||
\(92\) | 0.572097 | 0.0596452 | ||||||||
\(93\) | 2.58419 | 0.267968 | ||||||||
\(94\) | −2.47929 | −0.255719 | ||||||||
\(95\) | 1.39434 | 0.143056 | ||||||||
\(96\) | −2.14148 | −0.218564 | ||||||||
\(97\) | −3.20410 | −0.325327 | −0.162664 | − | 0.986682i | \(-0.552009\pi\) | ||||
−0.162664 | + | 0.986682i | \(0.552009\pi\) | |||||||
\(98\) | 17.0738 | 1.72471 | ||||||||
\(99\) | 3.75031 | 0.376920 | ||||||||
\(100\) | 4.15821 | 0.415821 | ||||||||
\(101\) | −16.0270 | −1.59475 | −0.797373 | − | 0.603487i | \(-0.793777\pi\) | ||||
−0.797373 | + | 0.603487i | \(0.793777\pi\) | |||||||
\(102\) | −0.220331 | −0.0218160 | ||||||||
\(103\) | −12.1875 | −1.20087 | −0.600434 | − | 0.799674i | \(-0.705005\pi\) | ||||
−0.600434 | + | 0.799674i | \(0.705005\pi\) | |||||||
\(104\) | 2.98785 | 0.292983 | ||||||||
\(105\) | −31.7974 | −3.10311 | ||||||||
\(106\) | 6.38183 | 0.619858 | ||||||||
\(107\) | 16.0032 | 1.54708 | 0.773542 | − | 0.633745i | \(-0.218483\pi\) | ||||
0.773542 | + | 0.633745i | \(0.218483\pi\) | |||||||
\(108\) | 3.02817 | 0.291385 | ||||||||
\(109\) | −12.5104 | −1.19828 | −0.599142 | − | 0.800643i | \(-0.704491\pi\) | ||||
−0.599142 | + | 0.800643i | \(0.704491\pi\) | |||||||
\(110\) | 7.15620 | 0.682317 | ||||||||
\(111\) | 4.07674 | 0.386947 | ||||||||
\(112\) | 4.90651 | 0.463621 | ||||||||
\(113\) | −6.12533 | −0.576222 | −0.288111 | − | 0.957597i | \(-0.593027\pi\) | ||||
−0.288111 | + | 0.957597i | \(0.593027\pi\) | |||||||
\(114\) | −0.986685 | −0.0924115 | ||||||||
\(115\) | 1.73131 | 0.161446 | ||||||||
\(116\) | −4.49268 | −0.417135 | ||||||||
\(117\) | 4.73858 | 0.438081 | ||||||||
\(118\) | −6.28216 | −0.578319 | ||||||||
\(119\) | 0.504816 | 0.0462764 | ||||||||
\(120\) | −6.48067 | −0.591601 | ||||||||
\(121\) | −5.40816 | −0.491651 | ||||||||
\(122\) | −10.0775 | −0.912377 | ||||||||
\(123\) | −25.1478 | −2.26750 | ||||||||
\(124\) | −1.20673 | −0.108367 | ||||||||
\(125\) | −2.54748 | −0.227854 | ||||||||
\(126\) | 7.78147 | 0.693228 | ||||||||
\(127\) | −3.67448 | −0.326058 | −0.163029 | − | 0.986621i | \(-0.552126\pi\) | ||||
−0.163029 | + | 0.986621i | \(0.552126\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −15.3232 | −1.34913 | ||||||||
\(130\) | 9.04198 | 0.793034 | ||||||||
\(131\) | 11.9430 | 1.04347 | 0.521733 | − | 0.853109i | \(-0.325286\pi\) | ||||
0.521733 | + | 0.853109i | \(0.325286\pi\) | |||||||
\(132\) | −5.06398 | −0.440763 | ||||||||
\(133\) | 2.26066 | 0.196024 | ||||||||
\(134\) | −0.866688 | −0.0748704 | ||||||||
\(135\) | 9.16399 | 0.788711 | ||||||||
\(136\) | 0.102887 | 0.00882250 | ||||||||
\(137\) | −15.3823 | −1.31420 | −0.657101 | − | 0.753803i | \(-0.728217\pi\) | ||||
−0.657101 | + | 0.753803i | \(0.728217\pi\) | |||||||
\(138\) | −1.22514 | −0.104291 | ||||||||
\(139\) | −17.3330 | −1.47017 | −0.735083 | − | 0.677977i | \(-0.762857\pi\) | ||||
−0.735083 | + | 0.677977i | \(0.762857\pi\) | |||||||
\(140\) | 14.8483 | 1.25491 | ||||||||
\(141\) | 5.30936 | 0.447129 | ||||||||
\(142\) | −10.2469 | −0.859905 | ||||||||
\(143\) | 7.06539 | 0.590837 | ||||||||
\(144\) | 1.58595 | 0.132162 | ||||||||
\(145\) | −13.5960 | −1.12909 | ||||||||
\(146\) | 0.484504 | 0.0400979 | ||||||||
\(147\) | −36.5632 | −3.01569 | ||||||||
\(148\) | −1.90370 | −0.156483 | ||||||||
\(149\) | 2.21301 | 0.181297 | 0.0906483 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906483 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(150\) | −8.90473 | −0.727068 | ||||||||
\(151\) | 14.7036 | 1.19656 | 0.598282 | − | 0.801286i | \(-0.295850\pi\) | ||||
0.598282 | + | 0.801286i | \(0.295850\pi\) | |||||||
\(152\) | 0.460748 | 0.0373716 | ||||||||
\(153\) | 0.163174 | 0.0131918 | ||||||||
\(154\) | 11.6025 | 0.934952 | ||||||||
\(155\) | −3.65187 | −0.293325 | ||||||||
\(156\) | −6.39843 | −0.512284 | ||||||||
\(157\) | 11.5889 | 0.924897 | 0.462449 | − | 0.886646i | \(-0.346971\pi\) | ||||
0.462449 | + | 0.886646i | \(0.346971\pi\) | |||||||
\(158\) | −1.79064 | −0.142456 | ||||||||
\(159\) | −13.6666 | −1.08383 | ||||||||
\(160\) | 3.02625 | 0.239246 | ||||||||
\(161\) | 2.80700 | 0.221222 | ||||||||
\(162\) | −11.2426 | −0.883303 | ||||||||
\(163\) | 4.95134 | 0.387819 | 0.193909 | − | 0.981019i | \(-0.437883\pi\) | ||||
0.193909 | + | 0.981019i | \(0.437883\pi\) | |||||||
\(164\) | 11.7432 | 0.916988 | ||||||||
\(165\) | −15.3249 | −1.19304 | ||||||||
\(166\) | −8.29759 | −0.644018 | ||||||||
\(167\) | 7.93708 | 0.614190 | 0.307095 | − | 0.951679i | \(-0.400643\pi\) | ||||
0.307095 | + | 0.951679i | \(0.400643\pi\) | |||||||
\(168\) | −10.5072 | −0.810648 | ||||||||
\(169\) | −4.07277 | −0.313290 | ||||||||
\(170\) | 0.311363 | 0.0238804 | ||||||||
\(171\) | 0.730723 | 0.0558798 | ||||||||
\(172\) | 7.15540 | 0.545594 | ||||||||
\(173\) | 10.4968 | 0.798055 | 0.399028 | − | 0.916939i | \(-0.369348\pi\) | ||||
0.399028 | + | 0.916939i | \(0.369348\pi\) | |||||||
\(174\) | 9.62100 | 0.729366 | ||||||||
\(175\) | 20.4023 | 1.54227 | ||||||||
\(176\) | 2.36471 | 0.178247 | ||||||||
\(177\) | 13.4531 | 1.01120 | ||||||||
\(178\) | 6.42816 | 0.481811 | ||||||||
\(179\) | −3.74264 | −0.279738 | −0.139869 | − | 0.990170i | \(-0.544668\pi\) | ||||
−0.139869 | + | 0.990170i | \(0.544668\pi\) | |||||||
\(180\) | 4.79948 | 0.357732 | ||||||||
\(181\) | 10.2544 | 0.762201 | 0.381100 | − | 0.924534i | \(-0.375545\pi\) | ||||
0.381100 | + | 0.924534i | \(0.375545\pi\) | |||||||
\(182\) | 14.6599 | 1.08666 | ||||||||
\(183\) | 21.5809 | 1.59530 | ||||||||
\(184\) | 0.572097 | 0.0421756 | ||||||||
\(185\) | −5.76107 | −0.423562 | ||||||||
\(186\) | 2.58419 | 0.189482 | ||||||||
\(187\) | 0.243298 | 0.0177917 | ||||||||
\(188\) | −2.47929 | −0.180821 | ||||||||
\(189\) | 14.8577 | 1.08074 | ||||||||
\(190\) | 1.39434 | 0.101156 | ||||||||
\(191\) | −13.3846 | −0.968474 | −0.484237 | − | 0.874937i | \(-0.660903\pi\) | ||||
−0.484237 | + | 0.874937i | \(0.660903\pi\) | |||||||
\(192\) | −2.14148 | −0.154548 | ||||||||
\(193\) | −13.0787 | −0.941427 | −0.470713 | − | 0.882286i | \(-0.656003\pi\) | ||||
−0.470713 | + | 0.882286i | \(0.656003\pi\) | |||||||
\(194\) | −3.20410 | −0.230041 | ||||||||
\(195\) | −19.3633 | −1.38663 | ||||||||
\(196\) | 17.0738 | 1.21956 | ||||||||
\(197\) | 0.464823 | 0.0331173 | 0.0165586 | − | 0.999863i | \(-0.494729\pi\) | ||||
0.0165586 | + | 0.999863i | \(0.494729\pi\) | |||||||
\(198\) | 3.75031 | 0.266523 | ||||||||
\(199\) | −15.2055 | −1.07789 | −0.538943 | − | 0.842342i | \(-0.681176\pi\) | ||||
−0.538943 | + | 0.842342i | \(0.681176\pi\) | |||||||
\(200\) | 4.15821 | 0.294030 | ||||||||
\(201\) | 1.85600 | 0.130912 | ||||||||
\(202\) | −16.0270 | −1.12766 | ||||||||
\(203\) | −22.0434 | −1.54714 | ||||||||
\(204\) | −0.220331 | −0.0154263 | ||||||||
\(205\) | 35.5378 | 2.48207 | ||||||||
\(206\) | −12.1875 | −0.849142 | ||||||||
\(207\) | 0.907317 | 0.0630629 | ||||||||
\(208\) | 2.98785 | 0.207170 | ||||||||
\(209\) | 1.08953 | 0.0753647 | ||||||||
\(210\) | −31.7974 | −2.19423 | ||||||||
\(211\) | −7.19882 | −0.495587 | −0.247793 | − | 0.968813i | \(-0.579705\pi\) | ||||
−0.247793 | + | 0.968813i | \(0.579705\pi\) | |||||||
\(212\) | 6.38183 | 0.438306 | ||||||||
\(213\) | 21.9437 | 1.50356 | ||||||||
\(214\) | 16.0032 | 1.09395 | ||||||||
\(215\) | 21.6540 | 1.47679 | ||||||||
\(216\) | 3.02817 | 0.206041 | ||||||||
\(217\) | −5.92082 | −0.401932 | ||||||||
\(218\) | −12.5104 | −0.847314 | ||||||||
\(219\) | −1.03756 | −0.0701117 | ||||||||
\(220\) | 7.15620 | 0.482471 | ||||||||
\(221\) | 0.307411 | 0.0206787 | ||||||||
\(222\) | 4.07674 | 0.273613 | ||||||||
\(223\) | 4.00568 | 0.268240 | 0.134120 | − | 0.990965i | \(-0.457179\pi\) | ||||
0.134120 | + | 0.990965i | \(0.457179\pi\) | |||||||
\(224\) | 4.90651 | 0.327830 | ||||||||
\(225\) | 6.59470 | 0.439647 | ||||||||
\(226\) | −6.12533 | −0.407451 | ||||||||
\(227\) | 19.7262 | 1.30927 | 0.654636 | − | 0.755944i | \(-0.272822\pi\) | ||||
0.654636 | + | 0.755944i | \(0.272822\pi\) | |||||||
\(228\) | −0.986685 | −0.0653448 | ||||||||
\(229\) | 3.34815 | 0.221252 | 0.110626 | − | 0.993862i | \(-0.464714\pi\) | ||||
0.110626 | + | 0.993862i | \(0.464714\pi\) | |||||||
\(230\) | 1.73131 | 0.114159 | ||||||||
\(231\) | −24.8465 | −1.63478 | ||||||||
\(232\) | −4.49268 | −0.294959 | ||||||||
\(233\) | −24.7957 | −1.62442 | −0.812211 | − | 0.583364i | \(-0.801736\pi\) | ||||
−0.812211 | + | 0.583364i | \(0.801736\pi\) | |||||||
\(234\) | 4.73858 | 0.309770 | ||||||||
\(235\) | −7.50296 | −0.489439 | ||||||||
\(236\) | −6.28216 | −0.408934 | ||||||||
\(237\) | 3.83464 | 0.249086 | ||||||||
\(238\) | 0.504816 | 0.0327224 | ||||||||
\(239\) | 14.0875 | 0.911242 | 0.455621 | − | 0.890174i | \(-0.349417\pi\) | ||||
0.455621 | + | 0.890174i | \(0.349417\pi\) | |||||||
\(240\) | −6.48067 | −0.418325 | ||||||||
\(241\) | 6.87248 | 0.442695 | 0.221348 | − | 0.975195i | \(-0.428954\pi\) | ||||
0.221348 | + | 0.975195i | \(0.428954\pi\) | |||||||
\(242\) | −5.40816 | −0.347650 | ||||||||
\(243\) | 14.9914 | 0.961697 | ||||||||
\(244\) | −10.0775 | −0.645148 | ||||||||
\(245\) | 51.6696 | 3.30105 | ||||||||
\(246\) | −25.1478 | −1.60337 | ||||||||
\(247\) | 1.37665 | 0.0875939 | ||||||||
\(248\) | −1.20673 | −0.0766274 | ||||||||
\(249\) | 17.7691 | 1.12607 | ||||||||
\(250\) | −2.54748 | −0.161117 | ||||||||
\(251\) | −21.6696 | −1.36777 | −0.683887 | − | 0.729588i | \(-0.739712\pi\) | ||||
−0.683887 | + | 0.729588i | \(0.739712\pi\) | |||||||
\(252\) | 7.78147 | 0.490186 | ||||||||
\(253\) | 1.35284 | 0.0850525 | ||||||||
\(254\) | −3.67448 | −0.230558 | ||||||||
\(255\) | −0.666778 | −0.0417552 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.662040 | 0.0412969 | 0.0206485 | − | 0.999787i | \(-0.493427\pi\) | ||||
0.0206485 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(258\) | −15.3232 | −0.953978 | ||||||||
\(259\) | −9.34050 | −0.580391 | ||||||||
\(260\) | 9.04198 | 0.560760 | ||||||||
\(261\) | −7.12517 | −0.441037 | ||||||||
\(262\) | 11.9430 | 0.737841 | ||||||||
\(263\) | 10.0437 | 0.619318 | 0.309659 | − | 0.950848i | \(-0.399785\pi\) | ||||
0.309659 | + | 0.950848i | \(0.399785\pi\) | |||||||
\(264\) | −5.06398 | −0.311666 | ||||||||
\(265\) | 19.3130 | 1.18639 | ||||||||
\(266\) | 2.26066 | 0.138610 | ||||||||
\(267\) | −13.7658 | −0.842454 | ||||||||
\(268\) | −0.866688 | −0.0529414 | ||||||||
\(269\) | −24.7612 | −1.50972 | −0.754858 | − | 0.655888i | \(-0.772294\pi\) | ||||
−0.754858 | + | 0.655888i | \(0.772294\pi\) | |||||||
\(270\) | 9.16399 | 0.557703 | ||||||||
\(271\) | −2.37168 | −0.144069 | −0.0720345 | − | 0.997402i | \(-0.522949\pi\) | ||||
−0.0720345 | + | 0.997402i | \(0.522949\pi\) | |||||||
\(272\) | 0.102887 | 0.00623845 | ||||||||
\(273\) | −31.3939 | −1.90005 | ||||||||
\(274\) | −15.3823 | −0.929280 | ||||||||
\(275\) | 9.83294 | 0.592949 | ||||||||
\(276\) | −1.22514 | −0.0737445 | ||||||||
\(277\) | −6.96992 | −0.418782 | −0.209391 | − | 0.977832i | \(-0.567148\pi\) | ||||
−0.209391 | + | 0.977832i | \(0.567148\pi\) | |||||||
\(278\) | −17.3330 | −1.03956 | ||||||||
\(279\) | −1.91381 | −0.114577 | ||||||||
\(280\) | 14.8483 | 0.887357 | ||||||||
\(281\) | 18.9864 | 1.13263 | 0.566317 | − | 0.824187i | \(-0.308368\pi\) | ||||
0.566317 | + | 0.824187i | \(0.308368\pi\) | |||||||
\(282\) | 5.30936 | 0.316168 | ||||||||
\(283\) | 26.5487 | 1.57816 | 0.789080 | − | 0.614291i | \(-0.210558\pi\) | ||||
0.789080 | + | 0.614291i | \(0.210558\pi\) | |||||||
\(284\) | −10.2469 | −0.608045 | ||||||||
\(285\) | −2.98596 | −0.176873 | ||||||||
\(286\) | 7.06539 | 0.417785 | ||||||||
\(287\) | 57.6179 | 3.40108 | ||||||||
\(288\) | 1.58595 | 0.0934530 | ||||||||
\(289\) | −16.9894 | −0.999377 | ||||||||
\(290\) | −13.5960 | −0.798384 | ||||||||
\(291\) | 6.86153 | 0.402230 | ||||||||
\(292\) | 0.484504 | 0.0283535 | ||||||||
\(293\) | 23.5503 | 1.37582 | 0.687912 | − | 0.725795i | \(-0.258528\pi\) | ||||
0.687912 | + | 0.725795i | \(0.258528\pi\) | |||||||
\(294\) | −36.5632 | −2.13241 | ||||||||
\(295\) | −19.0114 | −1.10689 | ||||||||
\(296\) | −1.90370 | −0.110650 | ||||||||
\(297\) | 7.16073 | 0.415507 | ||||||||
\(298\) | 2.21301 | 0.128196 | ||||||||
\(299\) | 1.70934 | 0.0988536 | ||||||||
\(300\) | −8.90473 | −0.514115 | ||||||||
\(301\) | 35.1080 | 2.02359 | ||||||||
\(302\) | 14.7036 | 0.846098 | ||||||||
\(303\) | 34.3215 | 1.97172 | ||||||||
\(304\) | 0.460748 | 0.0264257 | ||||||||
\(305\) | −30.4971 | −1.74626 | ||||||||
\(306\) | 0.163174 | 0.00932803 | ||||||||
\(307\) | −2.33030 | −0.132997 | −0.0664987 | − | 0.997787i | \(-0.521183\pi\) | ||||
−0.0664987 | + | 0.997787i | \(0.521183\pi\) | |||||||
\(308\) | 11.6025 | 0.661111 | ||||||||
\(309\) | 26.0993 | 1.48474 | ||||||||
\(310\) | −3.65187 | −0.207412 | ||||||||
\(311\) | 17.5037 | 0.992541 | 0.496271 | − | 0.868168i | \(-0.334702\pi\) | ||||
0.496271 | + | 0.868168i | \(0.334702\pi\) | |||||||
\(312\) | −6.39843 | −0.362240 | ||||||||
\(313\) | −25.6728 | −1.45111 | −0.725557 | − | 0.688162i | \(-0.758418\pi\) | ||||
−0.725557 | + | 0.688162i | \(0.758418\pi\) | |||||||
\(314\) | 11.5889 | 0.654001 | ||||||||
\(315\) | 23.5487 | 1.32682 | ||||||||
\(316\) | −1.79064 | −0.100732 | ||||||||
\(317\) | −19.5291 | −1.09686 | −0.548432 | − | 0.836195i | \(-0.684775\pi\) | ||||
−0.548432 | + | 0.836195i | \(0.684775\pi\) | |||||||
\(318\) | −13.6666 | −0.766384 | ||||||||
\(319\) | −10.6239 | −0.594823 | ||||||||
\(320\) | 3.02625 | 0.169173 | ||||||||
\(321\) | −34.2705 | −1.91279 | ||||||||
\(322\) | 2.80700 | 0.156428 | ||||||||
\(323\) | 0.0474051 | 0.00263769 | ||||||||
\(324\) | −11.2426 | −0.624590 | ||||||||
\(325\) | 12.4241 | 0.689164 | ||||||||
\(326\) | 4.95134 | 0.274229 | ||||||||
\(327\) | 26.7909 | 1.48154 | ||||||||
\(328\) | 11.7432 | 0.648408 | ||||||||
\(329\) | −12.1647 | −0.670659 | ||||||||
\(330\) | −15.3249 | −0.843607 | ||||||||
\(331\) | 24.5242 | 1.34797 | 0.673987 | − | 0.738743i | \(-0.264580\pi\) | ||||
0.673987 | + | 0.738743i | \(0.264580\pi\) | |||||||
\(332\) | −8.29759 | −0.455389 | ||||||||
\(333\) | −3.01917 | −0.165449 | ||||||||
\(334\) | 7.93708 | 0.434298 | ||||||||
\(335\) | −2.62282 | −0.143300 | ||||||||
\(336\) | −10.5072 | −0.573215 | ||||||||
\(337\) | 11.1072 | 0.605049 | 0.302525 | − | 0.953142i | \(-0.402171\pi\) | ||||
0.302525 | + | 0.953142i | \(0.402171\pi\) | |||||||
\(338\) | −4.07277 | −0.221529 | ||||||||
\(339\) | 13.1173 | 0.712433 | ||||||||
\(340\) | 0.311363 | 0.0168860 | ||||||||
\(341\) | −2.85356 | −0.154529 | ||||||||
\(342\) | 0.730723 | 0.0395130 | ||||||||
\(343\) | 49.4271 | 2.66881 | ||||||||
\(344\) | 7.15540 | 0.385793 | ||||||||
\(345\) | −3.70757 | −0.199609 | ||||||||
\(346\) | 10.4968 | 0.564310 | ||||||||
\(347\) | 24.3878 | 1.30920 | 0.654602 | − | 0.755974i | \(-0.272836\pi\) | ||||
0.654602 | + | 0.755974i | \(0.272836\pi\) | |||||||
\(348\) | 9.62100 | 0.515740 | ||||||||
\(349\) | −5.06912 | −0.271344 | −0.135672 | − | 0.990754i | \(-0.543319\pi\) | ||||
−0.135672 | + | 0.990754i | \(0.543319\pi\) | |||||||
\(350\) | 20.4023 | 1.09055 | ||||||||
\(351\) | 9.04770 | 0.482930 | ||||||||
\(352\) | 2.36471 | 0.126039 | ||||||||
\(353\) | −20.0993 | −1.06978 | −0.534888 | − | 0.844923i | \(-0.679646\pi\) | ||||
−0.534888 | + | 0.844923i | \(0.679646\pi\) | |||||||
\(354\) | 13.4531 | 0.715026 | ||||||||
\(355\) | −31.0099 | −1.64583 | ||||||||
\(356\) | 6.42816 | 0.340692 | ||||||||
\(357\) | −1.08106 | −0.0572155 | ||||||||
\(358\) | −3.74264 | −0.197805 | ||||||||
\(359\) | 24.8402 | 1.31102 | 0.655508 | − | 0.755188i | \(-0.272454\pi\) | ||||
0.655508 | + | 0.755188i | \(0.272454\pi\) | |||||||
\(360\) | 4.79948 | 0.252955 | ||||||||
\(361\) | −18.7877 | −0.988827 | ||||||||
\(362\) | 10.2544 | 0.538957 | ||||||||
\(363\) | 11.5815 | 0.607870 | ||||||||
\(364\) | 14.6599 | 0.768387 | ||||||||
\(365\) | 1.46623 | 0.0767461 | ||||||||
\(366\) | 21.5809 | 1.12805 | ||||||||
\(367\) | 27.8619 | 1.45438 | 0.727189 | − | 0.686437i | \(-0.240826\pi\) | ||||
0.727189 | + | 0.686437i | \(0.240826\pi\) | |||||||
\(368\) | 0.572097 | 0.0298226 | ||||||||
\(369\) | 18.6241 | 0.969531 | ||||||||
\(370\) | −5.76107 | −0.299504 | ||||||||
\(371\) | 31.3125 | 1.62566 | ||||||||
\(372\) | 2.58419 | 0.133984 | ||||||||
\(373\) | −15.6163 | −0.808580 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(374\) | 0.243298 | 0.0125806 | ||||||||
\(375\) | 5.45539 | 0.281715 | ||||||||
\(376\) | −2.47929 | −0.127860 | ||||||||
\(377\) | −13.4235 | −0.691343 | ||||||||
\(378\) | 14.8577 | 0.764198 | ||||||||
\(379\) | −0.436254 | −0.0224089 | −0.0112044 | − | 0.999937i | \(-0.503567\pi\) | ||||
−0.0112044 | + | 0.999937i | \(0.503567\pi\) | |||||||
\(380\) | 1.39434 | 0.0715282 | ||||||||
\(381\) | 7.86885 | 0.403133 | ||||||||
\(382\) | −13.3846 | −0.684815 | ||||||||
\(383\) | 2.41816 | 0.123562 | 0.0617811 | − | 0.998090i | \(-0.480322\pi\) | ||||
0.0617811 | + | 0.998090i | \(0.480322\pi\) | |||||||
\(384\) | −2.14148 | −0.109282 | ||||||||
\(385\) | 35.1119 | 1.78947 | ||||||||
\(386\) | −13.0787 | −0.665689 | ||||||||
\(387\) | 11.3481 | 0.576856 | ||||||||
\(388\) | −3.20410 | −0.162664 | ||||||||
\(389\) | −12.4124 | −0.629336 | −0.314668 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314668 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(390\) | −19.3633 | −0.980496 | ||||||||
\(391\) | 0.0588614 | 0.00297675 | ||||||||
\(392\) | 17.0738 | 0.862357 | ||||||||
\(393\) | −25.5757 | −1.29013 | ||||||||
\(394\) | 0.464823 | 0.0234174 | ||||||||
\(395\) | −5.41894 | −0.272657 | ||||||||
\(396\) | 3.75031 | 0.188460 | ||||||||
\(397\) | −18.4432 | −0.925639 | −0.462819 | − | 0.886453i | \(-0.653162\pi\) | ||||
−0.462819 | + | 0.886453i | \(0.653162\pi\) | |||||||
\(398\) | −15.2055 | −0.762181 | ||||||||
\(399\) | −4.84117 | −0.242362 | ||||||||
\(400\) | 4.15821 | 0.207910 | ||||||||
\(401\) | 27.7066 | 1.38360 | 0.691801 | − | 0.722088i | \(-0.256817\pi\) | ||||
0.691801 | + | 0.722088i | \(0.256817\pi\) | |||||||
\(402\) | 1.85600 | 0.0925687 | ||||||||
\(403\) | −3.60552 | −0.179604 | ||||||||
\(404\) | −16.0270 | −0.797373 | ||||||||
\(405\) | −34.0230 | −1.69062 | ||||||||
\(406\) | −22.0434 | −1.09399 | ||||||||
\(407\) | −4.50169 | −0.223140 | ||||||||
\(408\) | −0.220331 | −0.0109080 | ||||||||
\(409\) | 7.93041 | 0.392133 | 0.196067 | − | 0.980591i | \(-0.437183\pi\) | ||||
0.196067 | + | 0.980591i | \(0.437183\pi\) | |||||||
\(410\) | 35.5378 | 1.75509 | ||||||||
\(411\) | 32.9410 | 1.62486 | ||||||||
\(412\) | −12.1875 | −0.600434 | ||||||||
\(413\) | −30.8234 | −1.51672 | ||||||||
\(414\) | 0.907317 | 0.0445922 | ||||||||
\(415\) | −25.1106 | −1.23263 | ||||||||
\(416\) | 2.98785 | 0.146491 | ||||||||
\(417\) | 37.1183 | 1.81769 | ||||||||
\(418\) | 1.08953 | 0.0532909 | ||||||||
\(419\) | 8.49355 | 0.414937 | 0.207468 | − | 0.978242i | \(-0.433478\pi\) | ||||
0.207468 | + | 0.978242i | \(0.433478\pi\) | |||||||
\(420\) | −31.7974 | −1.55156 | ||||||||
\(421\) | −29.9497 | −1.45966 | −0.729829 | − | 0.683630i | \(-0.760400\pi\) | ||||
−0.729829 | + | 0.683630i | \(0.760400\pi\) | |||||||
\(422\) | −7.19882 | −0.350433 | ||||||||
\(423\) | −3.93203 | −0.191182 | ||||||||
\(424\) | 6.38183 | 0.309929 | ||||||||
\(425\) | 0.427826 | 0.0207526 | ||||||||
\(426\) | 21.9437 | 1.06317 | ||||||||
\(427\) | −49.4455 | −2.39283 | ||||||||
\(428\) | 16.0032 | 0.773542 | ||||||||
\(429\) | −15.1304 | −0.730503 | ||||||||
\(430\) | 21.6540 | 1.04425 | ||||||||
\(431\) | −15.3279 | −0.738319 | −0.369160 | − | 0.929366i | \(-0.620354\pi\) | ||||
−0.369160 | + | 0.929366i | \(0.620354\pi\) | |||||||
\(432\) | 3.02817 | 0.145693 | ||||||||
\(433\) | −1.71995 | −0.0826553 | −0.0413277 | − | 0.999146i | \(-0.513159\pi\) | ||||
−0.0413277 | + | 0.999146i | \(0.513159\pi\) | |||||||
\(434\) | −5.92082 | −0.284209 | ||||||||
\(435\) | 29.1156 | 1.39599 | ||||||||
\(436\) | −12.5104 | −0.599142 | ||||||||
\(437\) | 0.263593 | 0.0126094 | ||||||||
\(438\) | −1.03756 | −0.0495764 | ||||||||
\(439\) | −19.7870 | −0.944380 | −0.472190 | − | 0.881497i | \(-0.656536\pi\) | ||||
−0.472190 | + | 0.881497i | \(0.656536\pi\) | |||||||
\(440\) | 7.15620 | 0.341159 | ||||||||
\(441\) | 27.0782 | 1.28944 | ||||||||
\(442\) | 0.307411 | 0.0146221 | ||||||||
\(443\) | −17.0676 | −0.810907 | −0.405453 | − | 0.914116i | \(-0.632886\pi\) | ||||
−0.405453 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(444\) | 4.07674 | 0.193473 | ||||||||
\(445\) | 19.4533 | 0.922173 | ||||||||
\(446\) | 4.00568 | 0.189675 | ||||||||
\(447\) | −4.73912 | −0.224152 | ||||||||
\(448\) | 4.90651 | 0.231811 | ||||||||
\(449\) | 33.8704 | 1.59844 | 0.799221 | − | 0.601038i | \(-0.205246\pi\) | ||||
0.799221 | + | 0.601038i | \(0.205246\pi\) | |||||||
\(450\) | 6.59470 | 0.310877 | ||||||||
\(451\) | 27.7692 | 1.30760 | ||||||||
\(452\) | −6.12533 | −0.288111 | ||||||||
\(453\) | −31.4876 | −1.47941 | ||||||||
\(454\) | 19.7262 | 0.925795 | ||||||||
\(455\) | 44.3645 | 2.07984 | ||||||||
\(456\) | −0.986685 | −0.0462057 | ||||||||
\(457\) | 12.5249 | 0.585890 | 0.292945 | − | 0.956129i | \(-0.405365\pi\) | ||||
0.292945 | + | 0.956129i | \(0.405365\pi\) | |||||||
\(458\) | 3.34815 | 0.156449 | ||||||||
\(459\) | 0.311559 | 0.0145423 | ||||||||
\(460\) | 1.73131 | 0.0807228 | ||||||||
\(461\) | 15.6533 | 0.729048 | 0.364524 | − | 0.931194i | \(-0.381232\pi\) | ||||
0.364524 | + | 0.931194i | \(0.381232\pi\) | |||||||
\(462\) | −24.8465 | −1.15596 | ||||||||
\(463\) | −2.03844 | −0.0947344 | −0.0473672 | − | 0.998878i | \(-0.515083\pi\) | ||||
−0.0473672 | + | 0.998878i | \(0.515083\pi\) | |||||||
\(464\) | −4.49268 | −0.208568 | ||||||||
\(465\) | 7.82041 | 0.362663 | ||||||||
\(466\) | −24.7957 | −1.14864 | ||||||||
\(467\) | 18.8781 | 0.873574 | 0.436787 | − | 0.899565i | \(-0.356116\pi\) | ||||
0.436787 | + | 0.899565i | \(0.356116\pi\) | |||||||
\(468\) | 4.73858 | 0.219041 | ||||||||
\(469\) | −4.25241 | −0.196358 | ||||||||
\(470\) | −7.50296 | −0.346086 | ||||||||
\(471\) | −24.8175 | −1.14353 | ||||||||
\(472\) | −6.28216 | −0.289160 | ||||||||
\(473\) | 16.9204 | 0.778002 | ||||||||
\(474\) | 3.83464 | 0.176131 | ||||||||
\(475\) | 1.91589 | 0.0879069 | ||||||||
\(476\) | 0.504816 | 0.0231382 | ||||||||
\(477\) | 10.1213 | 0.463421 | ||||||||
\(478\) | 14.0875 | 0.644345 | ||||||||
\(479\) | −17.7215 | −0.809714 | −0.404857 | − | 0.914380i | \(-0.632679\pi\) | ||||
−0.404857 | + | 0.914380i | \(0.632679\pi\) | |||||||
\(480\) | −6.48067 | −0.295801 | ||||||||
\(481\) | −5.68796 | −0.259349 | ||||||||
\(482\) | 6.87248 | 0.313033 | ||||||||
\(483\) | −6.01114 | −0.273516 | ||||||||
\(484\) | −5.40816 | −0.245825 | ||||||||
\(485\) | −9.69642 | −0.440292 | ||||||||
\(486\) | 14.9914 | 0.680022 | ||||||||
\(487\) | 13.0609 | 0.591847 | 0.295924 | − | 0.955212i | \(-0.404373\pi\) | ||||
0.295924 | + | 0.955212i | \(0.404373\pi\) | |||||||
\(488\) | −10.0775 | −0.456188 | ||||||||
\(489\) | −10.6032 | −0.479493 | ||||||||
\(490\) | 51.6696 | 2.33420 | ||||||||
\(491\) | 34.4920 | 1.55660 | 0.778301 | − | 0.627892i | \(-0.216082\pi\) | ||||
0.778301 | + | 0.627892i | \(0.216082\pi\) | |||||||
\(492\) | −25.1478 | −1.13375 | ||||||||
\(493\) | −0.462239 | −0.0208182 | ||||||||
\(494\) | 1.37665 | 0.0619382 | ||||||||
\(495\) | 11.3494 | 0.510116 | ||||||||
\(496\) | −1.20673 | −0.0541837 | ||||||||
\(497\) | −50.2767 | −2.25522 | ||||||||
\(498\) | 17.7691 | 0.796254 | ||||||||
\(499\) | 13.7083 | 0.613667 | 0.306834 | − | 0.951763i | \(-0.400730\pi\) | ||||
0.306834 | + | 0.951763i | \(0.400730\pi\) | |||||||
\(500\) | −2.54748 | −0.113927 | ||||||||
\(501\) | −16.9971 | −0.759375 | ||||||||
\(502\) | −21.6696 | −0.967163 | ||||||||
\(503\) | 19.3078 | 0.860893 | 0.430446 | − | 0.902616i | \(-0.358356\pi\) | ||||
0.430446 | + | 0.902616i | \(0.358356\pi\) | |||||||
\(504\) | 7.78147 | 0.346614 | ||||||||
\(505\) | −48.5017 | −2.15830 | ||||||||
\(506\) | 1.35284 | 0.0601412 | ||||||||
\(507\) | 8.72176 | 0.387347 | ||||||||
\(508\) | −3.67448 | −0.163029 | ||||||||
\(509\) | 31.5399 | 1.39798 | 0.698991 | − | 0.715130i | \(-0.253633\pi\) | ||||
0.698991 | + | 0.715130i | \(0.253633\pi\) | |||||||
\(510\) | −0.666778 | −0.0295254 | ||||||||
\(511\) | 2.37722 | 0.105162 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.39522 | 0.0616006 | ||||||||
\(514\) | 0.662040 | 0.0292013 | ||||||||
\(515\) | −36.8824 | −1.62523 | ||||||||
\(516\) | −15.3232 | −0.674564 | ||||||||
\(517\) | −5.86280 | −0.257846 | ||||||||
\(518\) | −9.34050 | −0.410398 | ||||||||
\(519\) | −22.4787 | −0.986704 | ||||||||
\(520\) | 9.04198 | 0.396517 | ||||||||
\(521\) | 5.03364 | 0.220528 | 0.110264 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110264 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(522\) | −7.12517 | −0.311860 | ||||||||
\(523\) | −0.0738998 | −0.00323141 | −0.00161571 | − | 0.999999i | \(-0.500514\pi\) | ||||
−0.00161571 | + | 0.999999i | \(0.500514\pi\) | |||||||
\(524\) | 11.9430 | 0.521733 | ||||||||
\(525\) | −43.6911 | −1.90684 | ||||||||
\(526\) | 10.0437 | 0.437924 | ||||||||
\(527\) | −0.124157 | −0.00540836 | ||||||||
\(528\) | −5.06398 | −0.220381 | ||||||||
\(529\) | −22.6727 | −0.985770 | ||||||||
\(530\) | 19.3130 | 0.838904 | ||||||||
\(531\) | −9.96318 | −0.432365 | ||||||||
\(532\) | 2.26066 | 0.0980122 | ||||||||
\(533\) | 35.0868 | 1.51978 | ||||||||
\(534\) | −13.7658 | −0.595705 | ||||||||
\(535\) | 48.4296 | 2.09379 | ||||||||
\(536\) | −0.866688 | −0.0374352 | ||||||||
\(537\) | 8.01481 | 0.345864 | ||||||||
\(538\) | −24.7612 | −1.06753 | ||||||||
\(539\) | 40.3745 | 1.73905 | ||||||||
\(540\) | 9.16399 | 0.394355 | ||||||||
\(541\) | 1.21097 | 0.0520636 | 0.0260318 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260318 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(542\) | −2.37168 | −0.101872 | ||||||||
\(543\) | −21.9595 | −0.942374 | ||||||||
\(544\) | 0.102887 | 0.00441125 | ||||||||
\(545\) | −37.8598 | −1.62173 | ||||||||
\(546\) | −31.3939 | −1.34354 | ||||||||
\(547\) | 4.78244 | 0.204482 | 0.102241 | − | 0.994760i | \(-0.467399\pi\) | ||||
0.102241 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(548\) | −15.3823 | −0.657101 | ||||||||
\(549\) | −15.9825 | −0.682114 | ||||||||
\(550\) | 9.83294 | 0.419278 | ||||||||
\(551\) | −2.07000 | −0.0881848 | ||||||||
\(552\) | −1.22514 | −0.0521453 | ||||||||
\(553\) | −8.78581 | −0.373611 | ||||||||
\(554\) | −6.96992 | −0.296124 | ||||||||
\(555\) | 12.3372 | 0.523686 | ||||||||
\(556\) | −17.3330 | −0.735083 | ||||||||
\(557\) | 9.18550 | 0.389202 | 0.194601 | − | 0.980882i | \(-0.437659\pi\) | ||||
0.194601 | + | 0.980882i | \(0.437659\pi\) | |||||||
\(558\) | −1.91381 | −0.0810181 | ||||||||
\(559\) | 21.3792 | 0.904245 | ||||||||
\(560\) | 14.8483 | 0.627456 | ||||||||
\(561\) | −0.521019 | −0.0219974 | ||||||||
\(562\) | 18.9864 | 0.800893 | ||||||||
\(563\) | 14.2454 | 0.600373 | 0.300186 | − | 0.953881i | \(-0.402951\pi\) | ||||
0.300186 | + | 0.953881i | \(0.402951\pi\) | |||||||
\(564\) | 5.30936 | 0.223564 | ||||||||
\(565\) | −18.5368 | −0.779849 | ||||||||
\(566\) | 26.5487 | 1.11593 | ||||||||
\(567\) | −55.1619 | −2.31658 | ||||||||
\(568\) | −10.2469 | −0.429952 | ||||||||
\(569\) | −33.7678 | −1.41562 | −0.707811 | − | 0.706402i | \(-0.750317\pi\) | ||||
−0.707811 | + | 0.706402i | \(0.750317\pi\) | |||||||
\(570\) | −2.98596 | −0.125068 | ||||||||
\(571\) | −2.55408 | −0.106885 | −0.0534424 | − | 0.998571i | \(-0.517019\pi\) | ||||
−0.0534424 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(572\) | 7.06539 | 0.295419 | ||||||||
\(573\) | 28.6628 | 1.19741 | ||||||||
\(574\) | 57.6179 | 2.40493 | ||||||||
\(575\) | 2.37890 | 0.0992069 | ||||||||
\(576\) | 1.58595 | 0.0660812 | ||||||||
\(577\) | 2.53739 | 0.105633 | 0.0528164 | − | 0.998604i | \(-0.483180\pi\) | ||||
0.0528164 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(578\) | −16.9894 | −0.706666 | ||||||||
\(579\) | 28.0079 | 1.16397 | ||||||||
\(580\) | −13.5960 | −0.564543 | ||||||||
\(581\) | −40.7122 | −1.68903 | ||||||||
\(582\) | 6.86153 | 0.284420 | ||||||||
\(583\) | 15.0912 | 0.625012 | ||||||||
\(584\) | 0.484504 | 0.0200489 | ||||||||
\(585\) | 14.3401 | 0.592891 | ||||||||
\(586\) | 23.5503 | 0.972854 | ||||||||
\(587\) | −45.3043 | −1.86991 | −0.934955 | − | 0.354766i | \(-0.884561\pi\) | ||||
−0.934955 | + | 0.354766i | \(0.884561\pi\) | |||||||
\(588\) | −36.5632 | −1.50784 | ||||||||
\(589\) | −0.555998 | −0.0229095 | ||||||||
\(590\) | −19.0114 | −0.782687 | ||||||||
\(591\) | −0.995411 | −0.0409457 | ||||||||
\(592\) | −1.90370 | −0.0782415 | ||||||||
\(593\) | −30.1819 | −1.23942 | −0.619710 | − | 0.784831i | \(-0.712750\pi\) | ||||
−0.619710 | + | 0.784831i | \(0.712750\pi\) | |||||||
\(594\) | 7.16073 | 0.293808 | ||||||||
\(595\) | 1.52770 | 0.0626297 | ||||||||
\(596\) | 2.21301 | 0.0906483 | ||||||||
\(597\) | 32.5622 | 1.33268 | ||||||||
\(598\) | 1.70934 | 0.0699001 | ||||||||
\(599\) | 3.49153 | 0.142660 | 0.0713300 | − | 0.997453i | \(-0.477276\pi\) | ||||
0.0713300 | + | 0.997453i | \(0.477276\pi\) | |||||||
\(600\) | −8.90473 | −0.363534 | ||||||||
\(601\) | −2.92013 | −0.119115 | −0.0595573 | − | 0.998225i | \(-0.518969\pi\) | ||||
−0.0595573 | + | 0.998225i | \(0.518969\pi\) | |||||||
\(602\) | 35.1080 | 1.43089 | ||||||||
\(603\) | −1.37452 | −0.0559749 | ||||||||
\(604\) | 14.7036 | 0.598282 | ||||||||
\(605\) | −16.3665 | −0.665391 | ||||||||
\(606\) | 34.3215 | 1.39422 | ||||||||
\(607\) | 21.9260 | 0.889950 | 0.444975 | − | 0.895543i | \(-0.353213\pi\) | ||||
0.444975 | + | 0.895543i | \(0.353213\pi\) | |||||||
\(608\) | 0.460748 | 0.0186858 | ||||||||
\(609\) | 47.2055 | 1.91286 | ||||||||
\(610\) | −30.4971 | −1.23479 | ||||||||
\(611\) | −7.40775 | −0.299685 | ||||||||
\(612\) | 0.163174 | 0.00659591 | ||||||||
\(613\) | 19.2838 | 0.778864 | 0.389432 | − | 0.921055i | \(-0.372671\pi\) | ||||
0.389432 | + | 0.921055i | \(0.372671\pi\) | |||||||
\(614\) | −2.33030 | −0.0940434 | ||||||||
\(615\) | −76.1036 | −3.06879 | ||||||||
\(616\) | 11.6025 | 0.467476 | ||||||||
\(617\) | 38.9538 | 1.56822 | 0.784110 | − | 0.620622i | \(-0.213120\pi\) | ||||
0.784110 | + | 0.620622i | \(0.213120\pi\) | |||||||
\(618\) | 26.0993 | 1.04987 | ||||||||
\(619\) | −23.1883 | −0.932018 | −0.466009 | − | 0.884780i | \(-0.654309\pi\) | ||||
−0.466009 | + | 0.884780i | \(0.654309\pi\) | |||||||
\(620\) | −3.65187 | −0.146663 | ||||||||
\(621\) | 1.73240 | 0.0695190 | ||||||||
\(622\) | 17.5037 | 0.701833 | ||||||||
\(623\) | 31.5398 | 1.26362 | ||||||||
\(624\) | −6.39843 | −0.256142 | ||||||||
\(625\) | −28.5004 | −1.14001 | ||||||||
\(626\) | −25.6728 | −1.02609 | ||||||||
\(627\) | −2.33322 | −0.0931798 | ||||||||
\(628\) | 11.5889 | 0.462449 | ||||||||
\(629\) | −0.195866 | −0.00780969 | ||||||||
\(630\) | 23.5487 | 0.938202 | ||||||||
\(631\) | 21.4699 | 0.854704 | 0.427352 | − | 0.904085i | \(-0.359447\pi\) | ||||
0.427352 | + | 0.904085i | \(0.359447\pi\) | |||||||
\(632\) | −1.79064 | −0.0712280 | ||||||||
\(633\) | 15.4161 | 0.612737 | ||||||||
\(634\) | −19.5291 | −0.775599 | ||||||||
\(635\) | −11.1199 | −0.441280 | ||||||||
\(636\) | −13.6666 | −0.541915 | ||||||||
\(637\) | 51.0139 | 2.02124 | ||||||||
\(638\) | −10.6239 | −0.420603 | ||||||||
\(639\) | −16.2511 | −0.642885 | ||||||||
\(640\) | 3.02625 | 0.119623 | ||||||||
\(641\) | 10.4306 | 0.411985 | 0.205993 | − | 0.978554i | \(-0.433958\pi\) | ||||
0.205993 | + | 0.978554i | \(0.433958\pi\) | |||||||
\(642\) | −34.2705 | −1.35255 | ||||||||
\(643\) | −20.5756 | −0.811422 | −0.405711 | − | 0.914001i | \(-0.632976\pi\) | ||||
−0.405711 | + | 0.914001i | \(0.632976\pi\) | |||||||
\(644\) | 2.80700 | 0.110611 | ||||||||
\(645\) | −46.3717 | −1.82589 | ||||||||
\(646\) | 0.0474051 | 0.00186513 | ||||||||
\(647\) | 34.3624 | 1.35092 | 0.675462 | − | 0.737395i | \(-0.263944\pi\) | ||||
0.675462 | + | 0.737395i | \(0.263944\pi\) | |||||||
\(648\) | −11.2426 | −0.441652 | ||||||||
\(649\) | −14.8555 | −0.583128 | ||||||||
\(650\) | 12.4241 | 0.487313 | ||||||||
\(651\) | 12.6793 | 0.496943 | ||||||||
\(652\) | 4.95134 | 0.193909 | ||||||||
\(653\) | −5.38313 | −0.210658 | −0.105329 | − | 0.994437i | \(-0.533590\pi\) | ||||
−0.105329 | + | 0.994437i | \(0.533590\pi\) | |||||||
\(654\) | 26.7909 | 1.04761 | ||||||||
\(655\) | 36.1426 | 1.41221 | ||||||||
\(656\) | 11.7432 | 0.458494 | ||||||||
\(657\) | 0.768400 | 0.0299781 | ||||||||
\(658\) | −12.1647 | −0.474228 | ||||||||
\(659\) | −20.5577 | −0.800815 | −0.400407 | − | 0.916337i | \(-0.631131\pi\) | ||||
−0.400407 | + | 0.916337i | \(0.631131\pi\) | |||||||
\(660\) | −15.3249 | −0.596520 | ||||||||
\(661\) | 8.53375 | 0.331924 | 0.165962 | − | 0.986132i | \(-0.446927\pi\) | ||||
0.165962 | + | 0.986132i | \(0.446927\pi\) | |||||||
\(662\) | 24.5242 | 0.953162 | ||||||||
\(663\) | −0.658316 | −0.0255669 | ||||||||
\(664\) | −8.29759 | −0.322009 | ||||||||
\(665\) | 6.84134 | 0.265296 | ||||||||
\(666\) | −3.01917 | −0.116990 | ||||||||
\(667\) | −2.57025 | −0.0995205 | ||||||||
\(668\) | 7.93708 | 0.307095 | ||||||||
\(669\) | −8.57810 | −0.331648 | ||||||||
\(670\) | −2.62282 | −0.101328 | ||||||||
\(671\) | −23.8304 | −0.919963 | ||||||||
\(672\) | −10.5072 | −0.405324 | ||||||||
\(673\) | 14.7422 | 0.568269 | 0.284135 | − | 0.958784i | \(-0.408294\pi\) | ||||
0.284135 | + | 0.958784i | \(0.408294\pi\) | |||||||
\(674\) | 11.1072 | 0.427835 | ||||||||
\(675\) | 12.5917 | 0.484656 | ||||||||
\(676\) | −4.07277 | −0.156645 | ||||||||
\(677\) | −24.5160 | −0.942228 | −0.471114 | − | 0.882072i | \(-0.656148\pi\) | ||||
−0.471114 | + | 0.882072i | \(0.656148\pi\) | |||||||
\(678\) | 13.1173 | 0.503766 | ||||||||
\(679\) | −15.7209 | −0.603314 | ||||||||
\(680\) | 0.311363 | 0.0119402 | ||||||||
\(681\) | −42.2432 | −1.61876 | ||||||||
\(682\) | −2.85356 | −0.109269 | ||||||||
\(683\) | −17.0194 | −0.651229 | −0.325614 | − | 0.945503i | \(-0.605571\pi\) | ||||
−0.325614 | + | 0.945503i | \(0.605571\pi\) | |||||||
\(684\) | 0.730723 | 0.0279399 | ||||||||
\(685\) | −46.5508 | −1.77862 | ||||||||
\(686\) | 49.4271 | 1.88714 | ||||||||
\(687\) | −7.17000 | −0.273553 | ||||||||
\(688\) | 7.15540 | 0.272797 | ||||||||
\(689\) | 19.0679 | 0.726430 | ||||||||
\(690\) | −3.70757 | −0.141145 | ||||||||
\(691\) | 27.9825 | 1.06450 | 0.532251 | − | 0.846586i | \(-0.321346\pi\) | ||||
0.532251 | + | 0.846586i | \(0.321346\pi\) | |||||||
\(692\) | 10.4968 | 0.399028 | ||||||||
\(693\) | 18.4009 | 0.698992 | ||||||||
\(694\) | 24.3878 | 0.925747 | ||||||||
\(695\) | −52.4540 | −1.98970 | ||||||||
\(696\) | 9.62100 | 0.364683 | ||||||||
\(697\) | 1.20822 | 0.0457647 | ||||||||
\(698\) | −5.06912 | −0.191869 | ||||||||
\(699\) | 53.0996 | 2.00841 | ||||||||
\(700\) | 20.4023 | 0.771133 | ||||||||
\(701\) | −23.4286 | −0.884886 | −0.442443 | − | 0.896797i | \(-0.645888\pi\) | ||||
−0.442443 | + | 0.896797i | \(0.645888\pi\) | |||||||
\(702\) | 9.04770 | 0.341483 | ||||||||
\(703\) | −0.877125 | −0.0330814 | ||||||||
\(704\) | 2.36471 | 0.0891233 | ||||||||
\(705\) | 16.0675 | 0.605136 | ||||||||
\(706\) | −20.0993 | −0.756446 | ||||||||
\(707\) | −78.6365 | −2.95743 | ||||||||
\(708\) | 13.4531 | 0.505600 | ||||||||
\(709\) | 11.2857 | 0.423842 | 0.211921 | − | 0.977287i | \(-0.432028\pi\) | ||||
0.211921 | + | 0.977287i | \(0.432028\pi\) | |||||||
\(710\) | −31.0099 | −1.16378 | ||||||||
\(711\) | −2.83987 | −0.106504 | ||||||||
\(712\) | 6.42816 | 0.240906 | ||||||||
\(713\) | −0.690366 | −0.0258544 | ||||||||
\(714\) | −1.08106 | −0.0404575 | ||||||||
\(715\) | 21.3816 | 0.799628 | ||||||||
\(716\) | −3.74264 | −0.139869 | ||||||||
\(717\) | −30.1680 | −1.12665 | ||||||||
\(718\) | 24.8402 | 0.927029 | ||||||||
\(719\) | −36.1228 | −1.34715 | −0.673577 | − | 0.739117i | \(-0.735243\pi\) | ||||
−0.673577 | + | 0.739117i | \(0.735243\pi\) | |||||||
\(720\) | 4.79948 | 0.178866 | ||||||||
\(721\) | −59.7979 | −2.22699 | ||||||||
\(722\) | −18.7877 | −0.699206 | ||||||||
\(723\) | −14.7173 | −0.547342 | ||||||||
\(724\) | 10.2544 | 0.381100 | ||||||||
\(725\) | −18.6815 | −0.693813 | ||||||||
\(726\) | 11.5815 | 0.429829 | ||||||||
\(727\) | −30.6948 | −1.13841 | −0.569204 | − | 0.822196i | \(-0.692749\pi\) | ||||
−0.569204 | + | 0.822196i | \(0.692749\pi\) | |||||||
\(728\) | 14.6599 | 0.543332 | ||||||||
\(729\) | 1.62408 | 0.0601511 | ||||||||
\(730\) | 1.46623 | 0.0542677 | ||||||||
\(731\) | 0.736198 | 0.0272293 | ||||||||
\(732\) | 21.5809 | 0.797651 | ||||||||
\(733\) | −11.5334 | −0.425995 | −0.212997 | − | 0.977053i | \(-0.568323\pi\) | ||||
−0.212997 | + | 0.977053i | \(0.568323\pi\) | |||||||
\(734\) | 27.8619 | 1.02840 | ||||||||
\(735\) | −110.650 | −4.08137 | ||||||||
\(736\) | 0.572097 | 0.0210878 | ||||||||
\(737\) | −2.04946 | −0.0754930 | ||||||||
\(738\) | 18.6241 | 0.685562 | ||||||||
\(739\) | 11.9344 | 0.439015 | 0.219507 | − | 0.975611i | \(-0.429555\pi\) | ||||
0.219507 | + | 0.975611i | \(0.429555\pi\) | |||||||
\(740\) | −5.76107 | −0.211781 | ||||||||
\(741\) | −2.94806 | −0.108300 | ||||||||
\(742\) | 31.3125 | 1.14952 | ||||||||
\(743\) | 32.9627 | 1.20928 | 0.604642 | − | 0.796497i | \(-0.293316\pi\) | ||||
0.604642 | + | 0.796497i | \(0.293316\pi\) | |||||||
\(744\) | 2.58419 | 0.0947410 | ||||||||
\(745\) | 6.69712 | 0.245363 | ||||||||
\(746\) | −15.6163 | −0.571752 | ||||||||
\(747\) | −13.1596 | −0.481483 | ||||||||
\(748\) | 0.243298 | 0.00889586 | ||||||||
\(749\) | 78.5196 | 2.86904 | ||||||||
\(750\) | 5.45539 | 0.199203 | ||||||||
\(751\) | −33.4445 | −1.22041 | −0.610204 | − | 0.792244i | \(-0.708913\pi\) | ||||
−0.610204 | + | 0.792244i | \(0.708913\pi\) | |||||||
\(752\) | −2.47929 | −0.0904105 | ||||||||
\(753\) | 46.4051 | 1.69110 | ||||||||
\(754\) | −13.4235 | −0.488853 | ||||||||
\(755\) | 44.4969 | 1.61941 | ||||||||
\(756\) | 14.8577 | 0.540370 | ||||||||
\(757\) | 34.4527 | 1.25220 | 0.626102 | − | 0.779741i | \(-0.284649\pi\) | ||||
0.626102 | + | 0.779741i | \(0.284649\pi\) | |||||||
\(758\) | −0.436254 | −0.0158455 | ||||||||
\(759\) | −2.89709 | −0.105158 | ||||||||
\(760\) | 1.39434 | 0.0505780 | ||||||||
\(761\) | −30.8397 | −1.11794 | −0.558970 | − | 0.829188i | \(-0.688803\pi\) | ||||
−0.558970 | + | 0.829188i | \(0.688803\pi\) | |||||||
\(762\) | 7.86885 | 0.285058 | ||||||||
\(763\) | −61.3826 | −2.22220 | ||||||||
\(764\) | −13.3846 | −0.484237 | ||||||||
\(765\) | 0.493805 | 0.0178536 | ||||||||
\(766\) | 2.41816 | 0.0873716 | ||||||||
\(767\) | −18.7701 | −0.677750 | ||||||||
\(768\) | −2.14148 | −0.0772741 | ||||||||
\(769\) | 11.3229 | 0.408315 | 0.204157 | − | 0.978938i | \(-0.434555\pi\) | ||||
0.204157 | + | 0.978938i | \(0.434555\pi\) | |||||||
\(770\) | 35.1119 | 1.26535 | ||||||||
\(771\) | −1.41775 | −0.0510589 | ||||||||
\(772\) | −13.0787 | −0.470713 | ||||||||
\(773\) | 14.4054 | 0.518125 | 0.259063 | − | 0.965861i | \(-0.416586\pi\) | ||||
0.259063 | + | 0.965861i | \(0.416586\pi\) | |||||||
\(774\) | 11.3481 | 0.407899 | ||||||||
\(775\) | −5.01783 | −0.180246 | ||||||||
\(776\) | −3.20410 | −0.115021 | ||||||||
\(777\) | 20.0025 | 0.717587 | ||||||||
\(778\) | −12.4124 | −0.445008 | ||||||||
\(779\) | 5.41064 | 0.193856 | ||||||||
\(780\) | −19.3633 | −0.693316 | ||||||||
\(781\) | −24.2310 | −0.867055 | ||||||||
\(782\) | 0.0588614 | 0.00210488 | ||||||||
\(783\) | −13.6046 | −0.486188 | ||||||||
\(784\) | 17.0738 | 0.609778 | ||||||||
\(785\) | 35.0710 | 1.25174 | ||||||||
\(786\) | −25.5757 | −0.912257 | ||||||||
\(787\) | 12.1680 | 0.433742 | 0.216871 | − | 0.976200i | \(-0.430415\pi\) | ||||
0.216871 | + | 0.976200i | \(0.430415\pi\) | |||||||
\(788\) | 0.464823 | 0.0165586 | ||||||||
\(789\) | −21.5083 | −0.765716 | ||||||||
\(790\) | −5.41894 | −0.192797 | ||||||||
\(791\) | −30.0540 | −1.06860 | ||||||||
\(792\) | 3.75031 | 0.133261 | ||||||||
\(793\) | −30.1101 | −1.06924 | ||||||||
\(794\) | −18.4432 | −0.654525 | ||||||||
\(795\) | −41.3585 | −1.46684 | ||||||||
\(796\) | −15.2055 | −0.538943 | ||||||||
\(797\) | 26.1475 | 0.926193 | 0.463097 | − | 0.886308i | \(-0.346738\pi\) | ||||
0.463097 | + | 0.886308i | \(0.346738\pi\) | |||||||
\(798\) | −4.84117 | −0.171376 | ||||||||
\(799\) | −0.255087 | −0.00902434 | ||||||||
\(800\) | 4.15821 | 0.147015 | ||||||||
\(801\) | 10.1947 | 0.360214 | ||||||||
\(802\) | 27.7066 | 0.978355 | ||||||||
\(803\) | 1.14571 | 0.0404313 | ||||||||
\(804\) | 1.85600 | 0.0654560 | ||||||||
\(805\) | 8.49468 | 0.299398 | ||||||||
\(806\) | −3.60552 | −0.126999 | ||||||||
\(807\) | 53.0257 | 1.86659 | ||||||||
\(808\) | −16.0270 | −0.563828 | ||||||||
\(809\) | −52.7718 | −1.85536 | −0.927678 | − | 0.373381i | \(-0.878199\pi\) | ||||
−0.927678 | + | 0.373381i | \(0.878199\pi\) | |||||||
\(810\) | −34.0230 | −1.19545 | ||||||||
\(811\) | −33.7966 | −1.18676 | −0.593380 | − | 0.804922i | \(-0.702207\pi\) | ||||
−0.593380 | + | 0.804922i | \(0.702207\pi\) | |||||||
\(812\) | −22.0434 | −0.773571 | ||||||||
\(813\) | 5.07890 | 0.178125 | ||||||||
\(814\) | −4.50169 | −0.157784 | ||||||||
\(815\) | 14.9840 | 0.524866 | ||||||||
\(816\) | −0.220331 | −0.00771313 | ||||||||
\(817\) | 3.29684 | 0.115342 | ||||||||
\(818\) | 7.93041 | 0.277280 | ||||||||
\(819\) | 23.2498 | 0.812415 | ||||||||
\(820\) | 35.5378 | 1.24103 | ||||||||
\(821\) | −38.9190 | −1.35828 | −0.679142 | − | 0.734007i | \(-0.737648\pi\) | ||||
−0.679142 | + | 0.734007i | \(0.737648\pi\) | |||||||
\(822\) | 32.9410 | 1.14895 | ||||||||
\(823\) | 21.3175 | 0.743083 | 0.371541 | − | 0.928416i | \(-0.378829\pi\) | ||||
0.371541 | + | 0.928416i | \(0.378829\pi\) | |||||||
\(824\) | −12.1875 | −0.424571 | ||||||||
\(825\) | −21.0571 | −0.733113 | ||||||||
\(826\) | −30.8234 | −1.07248 | ||||||||
\(827\) | 40.3624 | 1.40354 | 0.701768 | − | 0.712405i | \(-0.252394\pi\) | ||||
0.701768 | + | 0.712405i | \(0.252394\pi\) | |||||||
\(828\) | 0.907317 | 0.0315314 | ||||||||
\(829\) | −20.5576 | −0.713994 | −0.356997 | − | 0.934105i | \(-0.616199\pi\) | ||||
−0.356997 | + | 0.934105i | \(0.616199\pi\) | |||||||
\(830\) | −25.1106 | −0.871602 | ||||||||
\(831\) | 14.9260 | 0.517776 | ||||||||
\(832\) | 2.98785 | 0.103585 | ||||||||
\(833\) | 1.75667 | 0.0608652 | ||||||||
\(834\) | 37.1183 | 1.28530 | ||||||||
\(835\) | 24.0196 | 0.831233 | ||||||||
\(836\) | 1.08953 | 0.0376824 | ||||||||
\(837\) | −3.65418 | −0.126307 | ||||||||
\(838\) | 8.49355 | 0.293405 | ||||||||
\(839\) | 6.90658 | 0.238441 | 0.119221 | − | 0.992868i | \(-0.461960\pi\) | ||||
0.119221 | + | 0.992868i | \(0.461960\pi\) | |||||||
\(840\) | −31.7974 | −1.09712 | ||||||||
\(841\) | −8.81580 | −0.303993 | ||||||||
\(842\) | −29.9497 | −1.03213 | ||||||||
\(843\) | −40.6591 | −1.40037 | ||||||||
\(844\) | −7.19882 | −0.247793 | ||||||||
\(845\) | −12.3252 | −0.424000 | ||||||||
\(846\) | −3.93203 | −0.135186 | ||||||||
\(847\) | −26.5352 | −0.911759 | ||||||||
\(848\) | 6.38183 | 0.219153 | ||||||||
\(849\) | −56.8537 | −1.95121 | ||||||||
\(850\) | 0.427826 | 0.0146743 | ||||||||
\(851\) | −1.08910 | −0.0373339 | ||||||||
\(852\) | 21.9437 | 0.751778 | ||||||||
\(853\) | −38.0363 | −1.30234 | −0.651169 | − | 0.758933i | \(-0.725721\pi\) | ||||
−0.651169 | + | 0.758933i | \(0.725721\pi\) | |||||||
\(854\) | −49.4455 | −1.69199 | ||||||||
\(855\) | 2.21135 | 0.0756267 | ||||||||
\(856\) | 16.0032 | 0.546977 | ||||||||
\(857\) | 29.9318 | 1.02245 | 0.511226 | − | 0.859446i | \(-0.329191\pi\) | ||||
0.511226 | + | 0.859446i | \(0.329191\pi\) | |||||||
\(858\) | −15.1304 | −0.516544 | ||||||||
\(859\) | 48.1047 | 1.64131 | 0.820655 | − | 0.571424i | \(-0.193609\pi\) | ||||
0.820655 | + | 0.571424i | \(0.193609\pi\) | |||||||
\(860\) | 21.6540 | 0.738396 | ||||||||
\(861\) | −123.388 | −4.20505 | ||||||||
\(862\) | −15.3279 | −0.522071 | ||||||||
\(863\) | 42.5551 | 1.44859 | 0.724296 | − | 0.689489i | \(-0.242165\pi\) | ||||
0.724296 | + | 0.689489i | \(0.242165\pi\) | |||||||
\(864\) | 3.02817 | 0.103020 | ||||||||
\(865\) | 31.7659 | 1.08007 | ||||||||
\(866\) | −1.71995 | −0.0584461 | ||||||||
\(867\) | 36.3825 | 1.23562 | ||||||||
\(868\) | −5.92082 | −0.200966 | ||||||||
\(869\) | −4.23435 | −0.143641 | ||||||||
\(870\) | 29.1156 | 0.987111 | ||||||||
\(871\) | −2.58953 | −0.0877429 | ||||||||
\(872\) | −12.5104 | −0.423657 | ||||||||
\(873\) | −5.08154 | −0.171984 | ||||||||
\(874\) | 0.263593 | 0.00891616 | ||||||||
\(875\) | −12.4992 | −0.422552 | ||||||||
\(876\) | −1.03756 | −0.0350558 | ||||||||
\(877\) | 19.5922 | 0.661580 | 0.330790 | − | 0.943704i | \(-0.392685\pi\) | ||||
0.330790 | + | 0.943704i | \(0.392685\pi\) | |||||||
\(878\) | −19.7870 | −0.667778 | ||||||||
\(879\) | −50.4326 | −1.70105 | ||||||||
\(880\) | 7.15620 | 0.241236 | ||||||||
\(881\) | 8.11407 | 0.273370 | 0.136685 | − | 0.990615i | \(-0.456355\pi\) | ||||
0.136685 | + | 0.990615i | \(0.456355\pi\) | |||||||
\(882\) | 27.0782 | 0.911770 | ||||||||
\(883\) | −43.6962 | −1.47049 | −0.735247 | − | 0.677800i | \(-0.762934\pi\) | ||||
−0.735247 | + | 0.677800i | \(0.762934\pi\) | |||||||
\(884\) | 0.307411 | 0.0103394 | ||||||||
\(885\) | 40.7126 | 1.36854 | ||||||||
\(886\) | −17.0676 | −0.573398 | ||||||||
\(887\) | −9.72075 | −0.326391 | −0.163195 | − | 0.986594i | \(-0.552180\pi\) | ||||
−0.163195 | + | 0.986594i | \(0.552180\pi\) | |||||||
\(888\) | 4.07674 | 0.136806 | ||||||||
\(889\) | −18.0289 | −0.604669 | ||||||||
\(890\) | 19.4533 | 0.652074 | ||||||||
\(891\) | −26.5855 | −0.890647 | ||||||||
\(892\) | 4.00568 | 0.134120 | ||||||||
\(893\) | −1.14233 | −0.0382266 | ||||||||
\(894\) | −4.73912 | −0.158500 | ||||||||
\(895\) | −11.3262 | −0.378593 | ||||||||
\(896\) | 4.90651 | 0.163915 | ||||||||
\(897\) | −3.66052 | −0.122221 | ||||||||
\(898\) | 33.8704 | 1.13027 | ||||||||
\(899\) | 5.42145 | 0.180816 | ||||||||
\(900\) | 6.59470 | 0.219823 | ||||||||
\(901\) | 0.656608 | 0.0218748 | ||||||||
\(902\) | 27.7692 | 0.924612 | ||||||||
\(903\) | −75.1832 | −2.50194 | ||||||||
\(904\) | −6.12533 | −0.203725 | ||||||||
\(905\) | 31.0323 | 1.03155 | ||||||||
\(906\) | −31.4876 | −1.04610 | ||||||||
\(907\) | 8.94554 | 0.297032 | 0.148516 | − | 0.988910i | \(-0.452550\pi\) | ||||
0.148516 | + | 0.988910i | \(0.452550\pi\) | |||||||
\(908\) | 19.7262 | 0.654636 | ||||||||
\(909\) | −25.4180 | −0.843062 | ||||||||
\(910\) | 44.3645 | 1.47067 | ||||||||
\(911\) | 54.8206 | 1.81629 | 0.908144 | − | 0.418658i | \(-0.137499\pi\) | ||||
0.908144 | + | 0.418658i | \(0.137499\pi\) | |||||||
\(912\) | −0.986685 | −0.0326724 | ||||||||
\(913\) | −19.6214 | −0.649373 | ||||||||
\(914\) | 12.5249 | 0.414286 | ||||||||
\(915\) | 65.3091 | 2.15905 | ||||||||
\(916\) | 3.34815 | 0.110626 | ||||||||
\(917\) | 58.5984 | 1.93509 | ||||||||
\(918\) | 0.311559 | 0.0102830 | ||||||||
\(919\) | 54.8896 | 1.81064 | 0.905320 | − | 0.424729i | \(-0.139631\pi\) | ||||
0.905320 | + | 0.424729i | \(0.139631\pi\) | |||||||
\(920\) | 1.73131 | 0.0570796 | ||||||||
\(921\) | 4.99030 | 0.164436 | ||||||||
\(922\) | 15.6533 | 0.515515 | ||||||||
\(923\) | −30.6163 | −1.00775 | ||||||||
\(924\) | −24.8465 | −0.817388 | ||||||||
\(925\) | −7.91596 | −0.260275 | ||||||||
\(926\) | −2.03844 | −0.0669873 | ||||||||
\(927\) | −19.3287 | −0.634839 | ||||||||
\(928\) | −4.49268 | −0.147480 | ||||||||
\(929\) | 51.8191 | 1.70013 | 0.850065 | − | 0.526677i | \(-0.176562\pi\) | ||||
0.850065 | + | 0.526677i | \(0.176562\pi\) | |||||||
\(930\) | 7.82041 | 0.256441 | ||||||||
\(931\) | 7.86672 | 0.257821 | ||||||||
\(932\) | −24.7957 | −0.812211 | ||||||||
\(933\) | −37.4838 | −1.22716 | ||||||||
\(934\) | 18.8781 | 0.617710 | ||||||||
\(935\) | 0.736281 | 0.0240790 | ||||||||
\(936\) | 4.73858 | 0.154885 | ||||||||
\(937\) | 30.6458 | 1.00115 | 0.500577 | − | 0.865692i | \(-0.333121\pi\) | ||||
0.500577 | + | 0.865692i | \(0.333121\pi\) | |||||||
\(938\) | −4.25241 | −0.138846 | ||||||||
\(939\) | 54.9779 | 1.79414 | ||||||||
\(940\) | −7.50296 | −0.244720 | ||||||||
\(941\) | −39.6461 | −1.29243 | −0.646214 | − | 0.763157i | \(-0.723648\pi\) | ||||
−0.646214 | + | 0.763157i | \(0.723648\pi\) | |||||||
\(942\) | −24.8175 | −0.808598 | ||||||||
\(943\) | 6.71823 | 0.218776 | ||||||||
\(944\) | −6.28216 | −0.204467 | ||||||||
\(945\) | 44.9632 | 1.46265 | ||||||||
\(946\) | 16.9204 | 0.550130 | ||||||||
\(947\) | −17.3138 | −0.562624 | −0.281312 | − | 0.959616i | \(-0.590770\pi\) | ||||
−0.281312 | + | 0.959616i | \(0.590770\pi\) | |||||||
\(948\) | 3.83464 | 0.124543 | ||||||||
\(949\) | 1.44763 | 0.0469919 | ||||||||
\(950\) | 1.91589 | 0.0621595 | ||||||||
\(951\) | 41.8212 | 1.35615 | ||||||||
\(952\) | 0.504816 | 0.0163612 | ||||||||
\(953\) | −5.11114 | −0.165566 | −0.0827831 | − | 0.996568i | \(-0.526381\pi\) | ||||
−0.0827831 | + | 0.996568i | \(0.526381\pi\) | |||||||
\(954\) | 10.1213 | 0.327688 | ||||||||
\(955\) | −40.5051 | −1.31071 | ||||||||
\(956\) | 14.0875 | 0.455621 | ||||||||
\(957\) | 22.7509 | 0.735431 | ||||||||
\(958\) | −17.7215 | −0.572554 | ||||||||
\(959\) | −75.4735 | −2.43717 | ||||||||
\(960\) | −6.48067 | −0.209163 | ||||||||
\(961\) | −29.5438 | −0.953026 | ||||||||
\(962\) | −5.68796 | −0.183387 | ||||||||
\(963\) | 25.3802 | 0.817866 | ||||||||
\(964\) | 6.87248 | 0.221348 | ||||||||
\(965\) | −39.5795 | −1.27411 | ||||||||
\(966\) | −6.01114 | −0.193405 | ||||||||
\(967\) | −30.5212 | −0.981497 | −0.490748 | − | 0.871301i | \(-0.663277\pi\) | ||||
−0.490748 | + | 0.871301i | \(0.663277\pi\) | |||||||
\(968\) | −5.40816 | −0.173825 | ||||||||
\(969\) | −0.101517 | −0.00326120 | ||||||||
\(970\) | −9.69642 | −0.311333 | ||||||||
\(971\) | −18.4468 | −0.591985 | −0.295993 | − | 0.955190i | \(-0.595650\pi\) | ||||
−0.295993 | + | 0.955190i | \(0.595650\pi\) | |||||||
\(972\) | 14.9914 | 0.480848 | ||||||||
\(973\) | −85.0445 | −2.72640 | ||||||||
\(974\) | 13.0609 | 0.418499 | ||||||||
\(975\) | −26.6060 | −0.852073 | ||||||||
\(976\) | −10.0775 | −0.322574 | ||||||||
\(977\) | −34.6632 | −1.10897 | −0.554487 | − | 0.832193i | \(-0.687085\pi\) | ||||
−0.554487 | + | 0.832193i | \(0.687085\pi\) | |||||||
\(978\) | −10.6032 | −0.339053 | ||||||||
\(979\) | 15.2007 | 0.485817 | ||||||||
\(980\) | 51.6696 | 1.65053 | ||||||||
\(981\) | −19.8409 | −0.633472 | ||||||||
\(982\) | 34.4920 | 1.10068 | ||||||||
\(983\) | −9.69657 | −0.309272 | −0.154636 | − | 0.987971i | \(-0.549421\pi\) | ||||
−0.154636 | + | 0.987971i | \(0.549421\pi\) | |||||||
\(984\) | −25.1478 | −0.801683 | ||||||||
\(985\) | 1.40667 | 0.0448203 | ||||||||
\(986\) | −0.462239 | −0.0147207 | ||||||||
\(987\) | 26.0504 | 0.829194 | ||||||||
\(988\) | 1.37665 | 0.0437969 | ||||||||
\(989\) | 4.09358 | 0.130168 | ||||||||
\(990\) | 11.3494 | 0.360707 | ||||||||
\(991\) | −16.9811 | −0.539423 | −0.269711 | − | 0.962941i | \(-0.586928\pi\) | ||||
−0.269711 | + | 0.962941i | \(0.586928\pi\) | |||||||
\(992\) | −1.20673 | −0.0383137 | ||||||||
\(993\) | −52.5183 | −1.66662 | ||||||||
\(994\) | −50.2767 | −1.59468 | ||||||||
\(995\) | −46.0156 | −1.45879 | ||||||||
\(996\) | 17.7691 | 0.563037 | ||||||||
\(997\) | 8.77329 | 0.277853 | 0.138926 | − | 0.990303i | \(-0.455635\pi\) | ||||
0.138926 | + | 0.990303i | \(0.455635\pi\) | |||||||
\(998\) | 13.7083 | 0.433928 | ||||||||
\(999\) | −5.76471 | −0.182387 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6046.2.a.f.1.12 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.f.1.12 | ✓ | 67 | 1.1 | even | 1 | trivial |